Existence theorems for certain kinetic equations and large data

DOI10.1007/BF00251505zbMath0654.76073OpenAlexW1981262427MaRDI QIDQ1108878

Leif Arkeryd

Publication date: 1988

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00251505

zbMATH Keywords

uniquenessBoltzmann equationcollision operatorbounded weight function

Mathematics Subject Classification ID

Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Kinetic theory of gases in equilibrium statistical mechanics (82B40)

Related Items (14)

A one dimensional Boltzmann equation with inelastic collisions ⋮ Weak solutions of the Boltzmann equation and energy conservation ⋮ Stability and exponential convergence for Boltzmann equation ⋮ Errata: Weak solutions of the Boltzmann equation and energy conservation ⋮ Global weak solutions of the Boltzmann equation in a slab with diffusive boundary conditions ⋮ On the StrongL¹Trend to Equilibrium for the Boltzmann Equation ⋮ Hypocoercivity for perturbation theory and perturbation of hypocoercivity for confined Boltzmann-type collisional equations ⋮ Global existence in \(L^ 1\) for the generalized Enskog equation. ⋮ Existence and trend to equilibrium of weak solutions of the boltzmann equation ⋮ A remarkable estimate for the solutions of the Boltzmann equation ⋮ Strict entropy production bounds and stability of the rate of convergence to equilibrium for the Boltzmann equation ⋮ On the one-dimensional Boltzmann equation for granular flows ⋮ Strong solutions of the Boltzmann equation in one spatial dimension ⋮ Trend to equilibrium of weak solutions of the Boltzmann equation in a slab with diffusive boundary conditions.

Cites Work

• Loeb solutions of the Boltzmann equation
• On the Boltzmann equation in unbounded space far from equilibrium, and the limit of zero mean free path
• Large-time behavior of discrete velocity Boltzmann equations
• The Boltzmann equation for weakly inhomogeneous data
• Global existence of solutions for a model Boltzmann equation
• On the Boltzmann equation. II: The full initial value problem
• On solution of the nonlinear Boltzmann equation with a cut-off in an unbounded domain
• New results on the Boltzmann equation in unbounded domains
• On the existence of global solutions of mixed problem for non-linear Boltzmann equation

This page was built for publication: Existence theorems for certain kinetic equations and large data